Square brackets in math mode without the bracket symbols

Yes, there is:

\lbrack
\rbrack

Or simply add the following command to your preamble.tex file in case you are on a template or if you are doing it from scratch then:

\documentclass{article}
\usepackage{mathtools}

\DeclarePairedDelimiter\Bracket{\lbrack}{\rbrack}

\newcommand*{\Value}{\frac{1}{2}x^2}%
\begin{document}
    \[\Bracket{\Value}\]
\end{document}